Jay-Z said the afternoon had to be like a dream for Derek Jeter, and his incredible 3,000th hit made the superstar rapper feel as if he were a kid.

The Grammy-winning musician and avowed Yankees fan was blown away by what Jeter did in the Yankees’ 5-4 victory over the Rays yesterday. He marveled over Jeter’s moment and said he predicted the homer when the captain came to the plate in the third inning against Tampa Bay left-hander David Price.

Jay-Z was only off in terms of the direction in which Jeter launched his shot.

“I actually called it,” Jay-Z said in the tunnel outside the Yankees clubhouse after the game. “But I called it to the wrong side, though. I thought he was going to hit the short porch, but he surprised everyone.

“I don’t even think he could have woke up and scripted a better day for himself,” he added. “To go 5-for-5 and first of all, to hit the homer for the 3,000, is just like the storybook ending.

“But that’s Derek Jeter for you. He’s just a winner. That’s how it happens.”

And for the man who recorded “Empire State of Mind,” being in the stadium for Jeter’s 3,000th hit was a moment of innocence.

“It turns you into a child,” he said. “My little godson’s back there. You turn into a child. Just to have [my godson] there as well, it’s just an amazing day.”

Jay-Z, wearing a Yankees cap, also raved about Jeter’s historic value to the team, putting him in “definitely, definitely the top tier” of players in franchise history. Asked how well he knows Jeter, Jay-Z said jokingly, “I’m a Yankees fan, so I know him as my best friend.”

As for predicting the homer, Jay-Z said, “I taped it as well, so I’m good.”